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sinc^2(w)
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How do you find the inverse Fourier transform from Fourier series coefficients?
no
What is the fourier transform of Tan function?
tanx = 2*(sin2x - sin4x + sin6x - ... )However, be warned that this series is very slow to converge.
What is the Fourier Series for x sinx from -pi to pi?
The word sine, not sinx is the trigonometric function of an angle. The answer to the math question what is the four series for x sine from -pi to pi, the answer is 24.3621.
Application of fourier transform?
the main application of fourier transform is the changing a function from frequency domain to time domain, laplaxe transform is the general form of fourier transform .
What is the history of fourier series?
It is quite complicated, and starts before Fourier. Trigonometric series arose in problems connected with astronomy in the 1750s, and were tackled by Euler and others. In a different context, they arose in connection with a vibrating string (e.g. a violin string) and solutions of the wave equation.Still in the 1750s, a controversy broke out as to what curves could be represented by trigonometric series and whether every solution to the wave equation could be represented as the sum of a trigonometric series; Daniel Bernoulli claimed that every solution could be so represented and Euler claimed that arbitrary curves could not necessarily be represented. The argument rumbled on for 20 years and dragged in other people, including Laplace. At that time the concepts were not available to settle the problem.Fourier worked on the heat equation (controlling the diffusion of heat in solid bodies, for example the Earth) in the early part of the 19th century, including a major paper in 1811 and a book in 1822. Fourier had a broader notion of function than the 18th-century people, and also had more convincing examples.Fourier's work was criticised at the time, and his insistence that discontinuous functions could be represented by trigonometric series contradicted a theorem in a textbook by the leading mathematician of the time, Cauchy.Nonetheless Fourier was right; Cauchy (and Fourier, and everyone else at that time) was missing the idea of uniform convergence of a series of functions. Fourier's work was widely taken up, and also the outstanding problems (just which functions can be represented by Fourier series?; how different can two functions be if they have the same Fourier series?) were slowly solved.Source: Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972, pages 478-481, 502-514, 671-678,and 964.
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
What is the difference between fourier series and discrete fourier transform?
Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
Can a discontinuous function be developed in a Fourier series?
Yes, a Fourier series can be used to approximate a function with some discontinuities. This can be proved easily.
Can every function be expanded in fouriers series?
no every function cannot be expressed in fourier series... fourier series can b usd only for periodic functions.
Can a discontinuous function be approximated by a fourier series?
Yes it can.
What is the difference between fourier series and fourier transform with real life example please?
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
What is harmonic as applied to fourier series?
When we do a Fourier transformation of a function we get the primary term which is the fundamental frequency and amplitude of the Fourier series. All the other terms, with higher frequencies and lower amplitudes, are the harmonics.
What is fourier series?
Consider a periodic function, generally defined by f(x+t) = f(x) for some t. Any periodic function can be written as an infinite sum of sines and cosines. This is called a Fourier series.
What are Joseph Fourier's works?
Fourier series and the Fourier transform
What is relation between laplace transform and fourier transform?
The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes ofvibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
